Examples
Compositum of Q(
√
2) and the subfield of Q(ζ532 ) of degree 53:
? bnr1 = bnrinit(Q, 8); H1 = Mat(2);
? bnr2 = bnrinit(Q, [53^2, [1]]); H2 = Mat(53);
? [bnr,H] = bnrcompositum([bnr1, H1], [bnr2, H2]);
? subcyclopclgp([bnr,H], 107)
time = 21 ms.
%18 = [107, [1, [1]], [0, []], ...]
The simpler direct construction is a disaster :
T = polcompositum(x^2-2,polsubcyclo(53^2,53), 2)
subcyclopclgp(T, 107)
will run for years trying to compute an [f, H] description (old efficiency bug, hard to fix).
Atelier 2022 (13/01/2022) – p. 11/13